Is a permanent teleportation circle only a destination, and not a point of departure?

The 5th-level spell teleportation circle says:

As you cast the spell, you draw a 10-foot-diameter circle on the ground inscribed with sigils that link your location to a permanent teleportation circle of your choice, whose sigil sequence you know and that is on the same plane of existence as you. A shimmering portal opens within the circle you drew and remains open until the end of your next turn.

[…]

You can create a permanent teleportation circle by casting this spell in the same location every day for one year. You need not use the circle to teleport when you cast the spell in this way.

The teleportation circle you draw seems to be a point of departure only when you cast it. When it’s a permanent teleportation circle, however, it doesn’t mention whether you can use it as a point of departure.

Can permanent teleportation circles only serve as destinations?

What happens after a creature of the chosen type penetrates my Magic Circle?

The Magic Circle spell description says:

  • The creature can’t willingly enter the cylinder by nonmagical means. If the creature tries to use teleportation or interplanar travel to do so, it must first succeed on a Charisma saving throw.
  • The creature has disadvantage on attack rolls against targets within the cylinder.
  • Targets within the cylinder can’t be charmed, frightened, or possessed by the creature.

What happens after a creature of the chosen type penetrates my Magic Circle? Does a character lose the other protections of the Circle for that creature?

I had always assumed no. I thought the creature could then try to knock or drag them out of the circle, but those attempts would still be made at disadvantage. And as long as they remained in the cylinder the character would still be immune to the creature’s charm, frighten or possession attempts.

An answer to a question about an inverted Magic Circle made me doubt my understanding. It made it sound that it is the barrier (the surface of the cylinder) that provides those defenses not just the state of being inside the field defined by the cylinder. I think my confusion lies in that the rules text doesn’t say something like, “As long as the creature is outside the circle it has disadvantage…” or “…can’t be charmed, frightened, or possessed by the creature as long as it is outside the circle.” The only criteria I see is that the targets have to be in the cylinder, nothing about where the creature is.

How to create buttons with circle mold in CSS

I am currently trying to recreate the following PNG into HTML/CSS

mock up image

The finished product is supposed to look just like this- 3 buttons spaced evenly in a circle “mold” (If you look around the element’s border, you can see how they outline a circle.)

enter image description here

How can I recreate this in CSS/HTML?

One solution would be to use clip-path, but I don’t know how to create a path for them. Another solution would be to just use images as backgrounds, but that has problems of its own.

ps. it can’t be replicated with border-radius either

Thanks!

Script doing sed in a file and circle the output

I’m trying to make a script for the following redirect:

Day 1

Dobritoiu    - Palmar Gae            - Icinga Petrisor    - Backup Popa        - Pupaza        - Vargatu        - Vasuica        - 

Day 2

Dobritoiu    -  Gae            - Palmar Petrisor    - Icinga Popa        - Backup Pupaza        - Vargatu        - Vasuica        - 

And etc till we have a circle. The output will be redirect via email. So far i’m here:

sed -e "1s/$  / Palmar/" -e "2s/$  / Icinga/" -e "3s/$  / Backup/" group_test | mail -s 'test' email_address 

. . .

sed -e "7s/$  / Palmar/" -e "1s/$  / Icinga/" -e "2s/$  / Backup/" group_test | mail -s 'test' email_address 

group_test contain my template:

Dobritoiu      -  Gae            -  Petrisor       -  Popa           - Pupaza         - Vargatu        - Vasuica        - 

Also I need to use some conditions:

1 – we have 3 weeks: first week the script need to run at 07:00 from Monday to Saturday second week the script need to run at 11:00 from Monday to Friday week three the script need to run at 15:00 from Monday to Friday And this 3 weeks is in a circle also.

2 – I think I need to have a different file:

Dobritoiu      - work Gae            - work Petrisor       - work Popa           - free Pupaza         - work Vargatu        - work Vasuica        - work 

or something like a calendar…in case of one of us if free in that day to be able to skip to the next person. Also would be nice if I can implement our monthly timesheet and / or the oncall days (oncall is only in week 2; 1 person per day) and etc 🙂

Do you have any ideas or suggestions?

Thank you in advance!

How to program circle position optimization algorithm?

I am quite new to programming and I need to write a program to determine which are the optimal uniform distribution of circles. To make an example of what I want, let’s say that I have to inks, one blue and one red. The goal is to define the color that I want to achieve (in this example different types of violet) and that the program tells me where do I have to put the drops of each ink in order to achieve that.

The inputs would be the drop size (on the surface), drop spacing along X (on the surface), drop spacing along Y (on the surface) and final color. The outputs of the program should be X and Y positions, and which drop (red or blue) should be placed in each position.

Could you please give me some ideas or point me towards the right direction? I have tried looking for similar algorithms, but was unsuccessful, so I decided to ask here in hope that you can help.

Thank you!

Trigonometric cancellation on the unit circle

Let $ z \in \mathbb{C}$ with $ |z|=1$ and $ z\ne 1$ . Now consider the sum $ $ S(N,p)=\sum_{k=0}^N k^p z^k,$ $ for some positive integers $ N,p$ .

An immediate upper bound on $ |S(N,p)|$ is $ $ |S(N,p)|\le C_1(p)N^{p+1},$ $ for some constant $ C_1$ depending only on $ p$ . I’m looking for a reference showing that accounting for the cancellation we have $ $ |S(N,p)|\le C_2(|1-z|,p)N^{p},$ $ for some explicit constant $ C_2$ depending only on $ p,|1-z|,$ and monotonic decreasing in $ |1-z|$ .

It is possible to prove such a bound using $ \sum_{k=0}^n k^p z^k = \left(z \frac{d}{dz}\right)^p \frac{1-z^{N+1}}{1-z}$ , but since it’s surly known I’m hoping for a reference.

Answers are much appreciated.

Flow over the circle

I’m trying to plot a vector field over a circle, Particularly the vector field in this plot:

VectorPlot[{(Sin[x])^3, 0}, {x, 0, 2 \[Pi]}, {y, -0.001, 0.001},  FrameTicks -> {{\[Pi]/2, \[Pi], 3 \[Pi]/2, 2 \[Pi]}, {-1, 1}}, Epilog ->  Plot[(Sin[x])^3, {x, 0, 2 \[Pi]}, PlotStyle -> Red,  Ticks -> None][[1]], PlotRange -> {{0, 2 \[Pi]}, {-1, 1}},  GridLines -> Automatic ] 

That was my way to plot a vector field over the line. But I want to plot this one-dimensional over a circle.